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Electrostatics
Electricity:
The branch of physics which deals with the study of charges at rest or in motion is
called electricity.

There are two branches of electricity which are as follows;

1. Electrostatics or static electricity

2. Electrodynamics or current electricity

1. Electrostatics:( Electro means charge and static means rest)

The branch of physics which deals with the study of properties of charges at rest is
known as electrostatics or static electricity.

2. Electrodynamics:( Electro means charge and dynamics means motion)

The branch of physics which deals with the study of properties of charges in motion
is called electrodynamics or current electricity.

Electric charge:
Electric charge is the physical property of matter that causes it to experience a force
when close to other electrically charged matter.

OR

 Charge is the intrinsic property associated with matter due to which it produces and
experiences electrical and magnetic effects.

Explanation:
The existence and nature of charge can be understood by performing the following
experiments;

Experiment 1: When an uncharged glass rod is brought near a suspended pith ball
as shown in the figure. The pith ball remains in its rest position showing that the gravitational

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force of attraction between the pith ball and the uncharged glass rod is too weak to cause any
movement in the pith ball.

Experiment 2: When a glass rod is rubbed with silk cloth and brought near the
suspended pith ball. The ball is seen to move towards the glass rod showing that glass rod
rubbed with silk cloth has the ability to attract small objects. Thus we say that glass rod is
charged.

Experiment 3: When an ebonite rod is rubbed with fur

is brought near a suspended pith ball. The ball is seen to move
towards the ebonite rod showing that the ebonite rod is able to
attract light objects when rubbed with fur. Thus the ebonite rod is
charged.

Experiment 4: when a charged glass rod is brought near a suspended charged glass
rod. The two glass rods repel each other showing that “like charges repel each other”.

Experiment 5: when a charged glass rod is brought near a suspended charged plastic rod. The
two rods attract each other showing that “unlike charges attract each other”.

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Electric nature of matter:

In general, the matter is electrically neutral. The amount of positive charges and
negative charges are equal in a neutral matter. The electric nature of matter can be explained
on the basis of structure of atom.

Structure of atom:
The smallest particle of matter which can or cannot exist free in nature is known as
atom. An atom consists of two parts; the central massive part is called nucleus which has
−27
positive charge consisting of protons and neutron. The proton has mass of 1.67×10 kg
while the mass of neutron is less than that of proton. Protons and neutron are collectively
−19
known as nucleons. The charge on each proton is equal to +1.6×10 C .

Electrons are the third particles which are revolving around the nucleus in circular
−31
orbits. The mass of electron is 9.11×10 kg and the charge on electron is −1.6×10 C .
−19

In a normal condition the number of electrons and number of protons are equal. Thus an atom
is electrically neutral under normal conditions.

Methods of charging an object: There are two methods due to which

an object can be charged.

a. Charging by rubbing b. Electrostatic Induction

a.Charging by rubbing:
The process in which two neutral objects can be charged by rubbing it with one
another is known as charging by rubbing.

Explanation:

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When glass rod is rubbed with silk cloth, some electrons from the surface atoms of
glass rod are transferred to silk cloth. This makes glass rod positively charged as it is now short
of electrons. The silk cloth becomes negatively charged as it gains excess of electrons.

Electrostatic induction:
The process, in which a charge body changes the charge distribution of a nearby
neutral body, is known as electrostatic induction.

Explanation:
When a charged body is brought near by a neutral body then the negative and
positive charges of neutral body rearranges themselves on the surface as well as in the interior
of the body. This effect is known as electrostatic induction.

This process occurs in insulator as well as in conductor. The neutral body regains its
original state when the charged body is removed.

Charging an insulator by induction:

When a charged comb is brought near a neutral insulator, the atoms of the insulator
induce itself in such a way that partial positive charge is produced on one end of the atom and
partial negative on the other end forms a dipole as shown in the figure. One dipole induces
another dipole. This phenomenon is known as polarization. In this way the comb attracts the
insulator towards itself.

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Charging by conductor by induction:

Consider a metallic sphere placed on insulating wooden stand as shown in the
figure. When a positively charged rod is brought near the sphere, then the charge distribution
of the sphere changes and the free electrons of the sphere will arrange themselves closer to the
rod. The quantity of the negative charge on one end of the sphere is equal to the positive
charge on the other end.

In this way the forces of attraction takes place between the rod and the sphere. Such
distribution of the charge on the sphere due to rod is known as charging a conductor by
induction.

Elecroscope:
It is an instrument used for detecting and testing the nature of charge on a body.

Construction:
A simple electroscope consists of a metal rod, which has metallic
disc at its upper end while its lower end is attached to gold leaves as
shown in the figure. The rod is fixed in a glass jar.

Charge Detection:
The presence of charge on a body can be detected by bringing it near the disc of an
uncharged electroscope as shown in the figure. If the body is charged then the leaves of the
electroscope will diverge to a definite extent, otherwise they would remain in their normal
position. Thus the presence of charge can be detected from the divergence of leaves of
electroscope due to electrostatic induction.

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Testing the nature of charge:

For testing the nature of charge on a body we first need to charge the electroscope
either positively or negatively by touching its disc with positively or negatively charged bodies.
Due to charging the leaves of the electroscope diverge to certain extent. If a charged body is
brought near the disc of the charged electroscope and the divergence of leaves increases it has
same charge as that on the electroscope. If the divergence of the leaves decreases then it has
opposite charge to that of the electroscope.

Coulomb’s law:
In 1785, Charles coulomb a French physicist performed various experiments and found
that the force between two charge bodies depends on distance between charges and
magnitude of charges. He stated it in the form of coulomb’s law.

Statement:
“The force of attraction or repulsion between any two bodies is directly proportional to
the product of charges and inversely proportional to the square of distance between them.”

Explanation:

Consider two point charges q1 and q 2 placed at a distance ‘r’ from one another as
shown in the figure. According to coulomb’s law, the force F of attraction or repulsion between
them is given by the relations

F ∝ q 1 q2 −−−−−−−−1
1
F ∝ 2 −−−−−−−−−−−2
r

Combining equation 1 and equation 2 we get

q1 q 2
F ∝
r2
q1 q2
F = k −−−−−−−−−3
r2

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Where “ k ” is constant of proportionality known as coulomb’s constant. The value of “ k

”depends upon the nature of medium and system of units in which F, q and r are measured. If
the medium is free space and system of units is SI, then the value of k is given by.

1 N .m
k = = 9 × 109 2
4 π εo C
2
−12 C
Where “
ε o ” is permittivity of free space and its value is 8.85 × 10 N . m . By substituting
the value of k we can also write equation 3 as;

1 q1 q2
F =
4 π εo r 2

Coulomb’s law is valid for point charges in which the size of charge bodies is small as compared
to the distance between them.

Coulomb’s law in dielectric:

An insulating material (other than air or vacuum) known as dielectric placed in
between the point charges the force between the charges is reduced by factor ε r known as
dielectric constant or relative permittivity. The value of dielectric constant is different for
¿
different dielectrics. The force F in presence of dielectric constant is given by.

1 q 1 q2
F¿ =
4 πε o ε r r 2

Unit of charge:
The SI unit of charge is coulomb.

Coulomb:
One coulomb is the amount of charge which repels an equal and similar charge with a
9
force of 9 ×10 N placed in air at a distance of 1 m from each other.

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Electric field:
The space or region around a charge where it experiences electric force on test
charges is known as electric field.

Explanation:
The region or space around the charge where it possesses special properties and
experience electric force on other charges is known as electric field or force field. It is a vector
field.

Electric field intensity:

The electric field intensity at a point is defined as;

“The force experienced on a unit positive test charge placed at a point with in the
electric field.”

Mathematically:

Consider a force
⃗F is acting on a test charge +q at a point with in the

electric field; then the electric field intensity

⃗E at that point is given by.

⃗E = F
⃗
+q
Electric field intensity is a vector quantity and its direction is same in which the test
charge will move. The unit of electric field intensity is N /C .

Electric lines of force:

The arbitrary lines used to represent the direction and magnitude of electric field is
known as electric lines of force.

Properties of electric lines of force:

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1. The lines of force are directed outward for positive charge and inward for negative

charge.
2. The field pattern of set up by the two equal negative and positive charges is shown in
the figure

3. The field pattern of set up by the two equal positive charges is shown in the figure.

4. The electric field between the two oppositely charged parallel plates is uniform at the
central region as shown in the figure.
5. No two lines intersect each other.

Electrostatic potential:
The work done in bringing a unit positive charge from a point of infinity to a point with
in the electric field is known as electrostatic potential at that point.

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Mathematically:
If W is the amount of work done in bringing a test charge +q from infinity to a certain
point in the field, the potential V at that point would be given by.

W
V =
+q

Potential difference:
Potential difference between two points is defined as the work done in moving a unit
positive charge from one point to another against the electric field.

Mathematically:
W AB
VB − V A =
+q

Electric potential is a scalar quantity. Its unit is volt

Volt:
When one joule work is done in bringing a unit positive charge from a point to another
point with in the electric field then the potential at that point will be one volt.

Capacitor:
The device used for the storage of electric charge is called capacitor.

Construction:
A simple capacitor consists of two parallel metallic plates separated by a small distance as
shown in the figure. Air or an insulating medium called dielectric is placed in between the
plates.

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Charging a capacitor:
The capacitor can be charged by placing one of the plates with the positive terminal of
the battery while the other is connected to the negative terminal of the battery. Charge +Q and
–Q appears on the plates. These charges attract each other due to mutual attraction and thus
remain on the surface of the plates after the removal of the battery.

Capacitance of a capacitor:
The ability of the capacitor to store charge is known as capacitance of a capacitor.

Explanation:
It is experimentally found that the charge Q on the plate of a capacitor is directly
proportional to the electric potential difference V between them.

Q ∝ V
Q = CV
OR
Q
⇒ C =
V
Where ‘C’ is constant of proportionality known as capacitance of the capacitor. The value of ‘C’
depends upon the area of the plates, distance between them and the medium between them.

Unit of capacitance:
The SI unit of capacitance is farad. Which is defined as “the capacity of that capacitor
which stores a charge of 1 coulomb by applying 1 volt potential difference between the plates”

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Combination of capacitors:
The connection of capacitors in electrical circuit is known as combination of
capacitors. The capacitor can be connected either in series or in parallel.

Series combination of capacitors:

In series combination of capacitors, the capacitors are connected plate to plate as
shown in the figure. The right plate of one capacitor is connected to the left plate of the next
capacitor so on. In series combination all the capacitors acquires the same amount of charge,
the potential across each capacitor is different.

Characteristic features:
Consider three capacitors are attached to one another in series as shown in the figure.

1. The battery supplies +Q to the left plate of the capacitor C 1 Due to electrostatic
induction –Q charge is induced on its right plate and +Q charge on the left plate of
capacitor C2 as shown in the figure. Thus the charge on each capacitor is same i-e Q.
2. The sum of potential difference across each capacitor V 1, V2, V3 is equal to the total
potential difference supplied by the battery. i-e
V = V 1 + V 2 V 3 −−−−−−−1
As Q = CV
Q
⇒V =
C
Q
V1 =
C1
Q
V2 =
C2
Q
V3 =
C3

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Putting all the values in equation 1
Q Q Q Q
= + +
C C1 C2 C3
Q 1 1 1
C
=Q
C1
+
(
C2
+
C3 )
1 1 1 1
= + +
C C1 C2 C3
Let “Ce” be the equivalent capacitance of all the three capacitors joined in series.

1 1 1 1
= + +
Ce C1 C2 C3
3. For ‘n’ capacitors the above equation becomes;
1 1 1 1 1
= + + . . .. .. . .. .. .. .+
Ce C1 C2 C3 Cn
4. The equivalent capacitance in series combination is less than any individual capacitance
in the combination.

Parallel combination of capacitors:

In parallel combination of capacitors, all the left plates of all the capacitors are
connected to one point while the right plates are connected to the other as shown in the figure.
A battery of ‘V’ volts is applied to the both points.

In parallel combination of capacitors, the potential difference across each capacitor is

the same while the charge stored in each capacitor is different.

Characteristic features:
1. In this type of capacitor the potential difference across each capacitor is same. i.e

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V = V 1 = V 2 = V 3 −−−−−−−1
2. The charge Q given at point A is distributed over all the capacitors. i.e
Q = Q1 + Q2 + Q3 −−−−−−−1
As Q=C V
Q 1 = C1 V 1
Q 2 = C2 V 2
Therefore
Q 3 = C3 V 3

Putting in above equation we get;

C V = C 1 V + C2 V + C 3 V
C V = (C 1 + C 2 + C 3) V
C = C 1 + C 2 + C 3−−−−−−−2
3. For ‘n’ capacitors we can write equation 2 as

C = C 1 + C 2 + C 3 .............+C n
4. The equivalent capacitance in parallel combination is greater than any individual
capacitance in the combination.

Different types of capacitors:

Capacitors are classified into various types depending upon their construction and
nature of dielectric used in them. Here we will discuss the type of capacitors based on
capacity.
1.Fixed capacitor:
Those capacitors whose plates are immovable are known as fixed capacitors. The
capacitance of such capacitors remains constant and cannot be varied. For example
paper capacitor, oil, mica or electrolyte.
2.Variable capacitor:
The capacitors in which the area of the plates facing each other can be changed
are known as variable capacitors. The capacitance of such capacitors does not remain
constant and can be varied. For example; the capacitors used in the tuning of radio.

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Practical applications of electrostatics:

The practical applications of electrostatics are as follows;

1.Electro painting:
Electrostatic is used in applying paints on the surfaces of different articles such
as refrigerators, metallic furniture, cars etc. it has become a standard technology.
For this purpose the body is earthed electrically. The particles of the paint
emerging out of the nozzle of the spraying, they acquire positive charge due to friction.
Negative charge is induced on the surface of the body. Thus a firm coating of paint is
formed on the surface of the body due to force of attraction.
2.Dust Extraction:
Electrostatic phenomenon is used for the separation of smoke and dust particles
from air coming out of various industries.
Highly positively charged Wire gauze is fixed between two metallic plates which
are grounded. Due to electrostatic induction negative charges are induced on the inner
surface of the metallic plates.
The gas containing dust and smoke particles become ionized after passing
through the gauze which is trapped by the negatively charged plates. Thus the dust and
smoke particles are separated from the air.

CONCEPTUAL QUESTIONS:
1. A balloon is negatively charged by rubbing and then clings to the wall. Does this mean
that the wall is positively charged? Why does the balloon eventually fall?

Ans. A negatively charged balloon first cling to the wall, because due to its electric field the
point of contact on the wall polarized positively due to electrostatic induction and attract the
balloon due to electrostatic force of attraction and thus clings.

Later on the balloon is neutralized because the wall is grounded and due to gravity the balloon
eventually falls.

2. Why is it not a good idea to seek shelter under a tree during a lightning storm?

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Ans: When charged clouds pass over a tall tree, then an opposite charge is induced on the tall
tree due to phenomenon of electrostatic induction. As a result electrostatic force of attraction
exist between the tree and the clouds due to which there is a greater possibility of for lightning
discharge to take place between the tree and the clouds. Therefore it is not a good idea to seek
shelter under a tree during a lightning storm.

3. A charged comb often attracts small bits of dry paper that then fly away when they touch
the comb. Explain?

Ans: When comb is brought near the bits, due to polarization, bits gets oppositely charged,
hence they are attracted by the comb. When they touch the comb, at point of contact the
charge is neutralized but the further points on the comb and bits have similar static charges so
due to repulsion fly away.

4. Define the term volt?

Ans: Volt is the SI unit of potential difference. It is defined as;

“If one joule of work is done in carrying one coulomb of charge from one point to
another against the electric field, then the potential difference between these two points will
be one volt.

Mathematically:

1j
1v =
1C

5. What is meant by charging of an object electrically?

Ans: When positive and negative charge appears on a body, it means that the object is charged
electrically. When the number of protons and electrons in an object are equal then the object is
electrically neutral. Now when electrons are added to the body or removed from the body then
the neutrality of the body is disturbed and is said to be charged.

Negative charge appears on the body if the number of protons exceeds the number of
protons while positive charge appears if the number of protons exceeds the number of
electrons.

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6. Two isolated copper spheres A, B are initially uncharged. They are placed near each other
as shown in the figure. What is the charge distribution on A when B is given a negative
charge?

Ans: When the negative charged sphere ‘B’ is brought near neutral sphere ‘A’, then charge is
induced on sphere A due to electrostatic induction. The positive charges on sphere A are
arranged on the side which is closer to A while the negative charges are arranged to the left
side of the sphere as shown in the figure.

7. Why electric charge is produced on bodies by friction?

Ans: When two bodies are rubbed together, then electrons are transferred from one body to
another due to friction. The body which loses electrons becomes positively charged while the
body which gain electron becomes negatively charged.

8. Two capacitors with capacitance 1μ F and 0.01μ F are charged to the same
potential? Which will give more intense shocked if touched?

Ans: Given data:

C1 = 1 μ F
= 1 × 10−6 F
= 10−6 F
C2 = 0 . 01μF
= 0 . 01 × 10−6 F
= 10−8 F
V1 = V2 = V

Also we know that;

Q 1 = C1 V and Q 2 = C2 V

Putting the values we get;

Q1 = 10−6 V and Q2 = 10−8 V

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From above equations it is clear that Q 1 > Q 2 for the same potential. Therefore the

capacitor of capacitance 1μ F will give more intense shock when touched.

9. As shown in the figure a chain hanging from the rear side of the petrol supply tanker.
What is its purpose?

Ans: Petrol is highly inflammable fluid. The chain should be touching the ground to keep
tanker’s body at zero potential and avoid a spark discharge due to which petrol can catch fire.

10. The tyres of an aircraft are made from special rubber that conducts electricity. Explain
why?

Ans: Aircraft’s when moving in air with high speed become charged due to friction due to
friction with air molecules and with various cloud. When the aircraft is landing and touches the
ground, the charges flows to the ground through tyres, the aircraft body becomes neutral and
thus avoids the sparking. In this way the aircraft remains in safe and sound condition.

Written and composed by:

SIR SULTAN
M.Sc.in APPLIED PHYSICS
&
ELECTRONIC ENGINEER

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